An Arecibo HI Science vision While the NSF panel was reviewing the Arecibo Program Plan in December 2008, it asked us in a face-to-face meeting to justify the large fraction of survey time spent on HI science. The immediate answer to this is that telescope time is allocated to the best submitted programs, and we constantly receive HI proposals. With respect to the ALFA surveys, moreover, pALFA has thus far used the 100 MHz bandwidth WAPP spectrometers, as the 300 MHz offered by the MOCK spectrometers was not available, so pALFA has only been asking for a modest time allocation. pALFA's ambitions have also been restrained by their immense, data-processing constraints. And the other major nonHI project, GALFACTS, has only just reached the telescope. However, an intrinsically compelling HI Science case exists. I expand here on the outline answer I made to the NSF panel, which is perhaps a personal, bystander's appraisal. With the decadal survey upon us, comments are welcome. The Maximum Entropy Principle mandates the Gaussian distribution as the statistical distribution function for non-interacting particles (Nakamura, T. K. ApJ 531, 739; 2000). When applied to a non-rotating, self-gravitating system, the resulting mass distribution is the isothermal sphere (eg Binney & Tremaine in Galactic Dynamics, chapter 9). This is characterized by a constant one dimensional rms velocity σ. Its mass within any radius r, M(r), is then strictly proportional to r, while its magnitude is set by σ. Hence M(r) for a system in long term equilibrium is set entirely by the parameters of the isothermal sphere: it is completely independent of the exact nature of the non-interacting mass, whether composed of stars, black holes, dark matter particles, or a mixture of them all. Under the ΛCDM paradigm non-interacting particles provide most of the mass of a galaxy, the majority in the form of dark matter, with most of the visibly identifiable baryons located in stars. We therefore expect the essential mass-distribution of a galaxy to follow that of an isothermal sphere. This is readily seen to be so. Spiral galaxies have extended flat rotation curves: the rotation velocity V(r) in almost every well-studied galaxy is constant after some finite radius to the limit of observation, as mandated by the underlying isothermal sphere. However, the rotation curve should then also be a step function through the nucleus. Since this is an unseen idealization, the extent of the departure of the rotation curve from that of a step function is a measure of the degree to which it departs from large-scale dynamical equilibrium near the nucleus. Moreover, since dynamical equilibrium is established most quickly in the nuclear regions of an isothermal sphere composed of a single mass species, I contend that this circumstance points to the existence of active dynamical processes that are recruiting baryons to the central regions of every spiral galaxy at the expense of dark matter. How do HI studies fit into this scenario? Most baryons in the Universe are ionized and located in either the intergalactic medium or the halos of galaxies. As these baryons cool en route to forming stars, they must undergo a phase transition to neutral hydrogen (HI), and may then subsequently undergo a phase transition to molecular hydrogen, before being incorporated into stars. So HI studies are necessary, both to understanding the primary processes of galaxy formation and assembly, and to understanding the precursor steps to star formation. HI observers study these processes in two contexts at Arecibo. The first is via the integral properties of a galaxy, which may be modified by mergers, by its intrinsic size, and by its environment: this is the robust approach used by eALFA. The second context is by studying the multitude of processes involved in our Galaxy's interstellar medium (ISM), as it is buffetted by accretion, star formation, and conditioned by turbulence and magnetic fields. This approach is followed by gALFA, as it explores the multitude of processes involved in our Galaxy's gas economy. The behaviour of the ISM is affected by large-scale turbulence, and by the presence of cosmic rays and magnetic fields, quite apart from the injection of energy from supernova outbursts, bursts of star formation, as well as from sundry other denizens of the Galactic zoo (O-B stars, µquasars, the central black hole, Galactic γ & X-ray sources, etc). Our Galaxy is much the best laboratory for these explorations, as it is close, allows better angular resolution, and potentially allows for the identification of many of the sources of energy injected into the ISM. This can be an embarrassment of riches. Most HI studies of our Galaxy depend on first completing a mapping survey, so that the HI column density is determined as a function of position and velocity. Arecibo is ideal for this, given its sensitivity, angular resolution, and complement of high-resolution spectrometers, now it is equipped with ALFA. gALFA exploits these capabilities. For instance Stanimirovic et al., ApJ, 680, 276 (2008) examined the northern extremity of the Magellanic Stream, and find that its tail branches off into four sub-streams, which is consistent with some tidal-model predictions. They also examined the numerous individual HI clouds in this region, and suggest that these may have been created by thermal instabilities, which is one context for gathering data on the HI/ionized gas phase transition. Likewise the accompanying item here by Carl Heiles describes the interaction of an in-falling HVC with Galactic Disk HI, an example of baryon recruitment. Extra galactic HI studies have long focused on the formation and evolution of galaxies. One major topic for Arecibo is the accretion of HI, and the resulting opportunities for delineating the mass, size and evolution of galaxies within the radial range of detectable baryons. Another is to suss out the lower limits to the HI mass of low mass galaxies, and to whether any of these can be found in the voids of the galaxy distribution. Yet another is to explore the limits to the detection of HI emission from gas-rich non-interacting disk galaxies in relatively isolated fields selected from the initial installments of the Sloan Digital Sky Survey (SDSS). The study by Catinella et al. (2008) pioneers the use of Arecibo in detecting galaxies in the redshift interval 0.17−0.25 (2−3 Gyr look-back time), with MHI = (3 − 8) 1010 M⊙. Ten galaxies were detected with on source integrations of up to three hours, including one with the largest z ~ 0.25 for detected HI emission to date. This program shows that we can study the HI properties of field galaxies at cosmological distances. Finally, the mapping of the distribution of galaxies in position and redshift delineates the large scale structure of baryon concentrations in the local Universe. The figure below, courtesy of Riccardo Giovanelli, shows that HI observations complement and augment optical studies of large scale structure. Figure is 3.2 from the current APRPP (Jill will have) Radial distribution of 5670 galaxies with measured radial velocities cz < 8000 km s-1 in the ALFALFA strip from 7h:30m < RA. < 16h:30m and +08° < Decl. <+16°. Different colors denote galaxies whose redshifts are drawn from, respectively, optical only (red), HI only (blue) and both (green). The HI—rich galaxies trace the same structures seen by optical surveys; the few ‘void” galaxies seen here are gas rich as expected.